Message Passing for Dynamic Network Energy Management

TL;DR

This paper introduces a decentralized message passing algorithm for large-scale, dynamic energy management in networks of diverse devices, enabling efficient and scalable optimization without global coordination.

Contribution

It develops a novel decentralized iterative method for solving large dynamic energy management problems using message passing, applicable to complex networks with convex objectives.

Findings

Converges for convex device objectives and constraints.

Solves a 30-million-variable problem in under an hour serially.

Decentralized implementation reduces solve time to under a second.

Abstract

We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints, over a given time horizon. This is a large optimization problem, with variables for consumption or generation in each time period for each device. In this paper we develop a decentralized method for solving this problem. The method is iterative: At each step, each device exchanges simple messages with its neighbors in the network and then solves its own optimization problem, minimizing its own objective function, augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized, and needs no global coordination other than synchronizing iterations; the problems to be solved by each device can typically be solved extremely efficiently and in parallel. The method is fast enough that even a serial implementation can solve substantial problems in reasonable time frames. We report results for several numerical experiments, demonstrating the method's speed and scaling, including the solution of a problem instance with over 30 million variables in 52 minutes for a serial implementation; with decentralized computing, the solve time would be less than one second.